In many applications in the fields of computation and numerical analysis, the value of a function at a desired domain coordinate must be approximated from known values of the function at other points in the domain. As an example, air pressure (the function) may be known at a set of locations on the earth ("location" comprising the domain), and from these known pressures, one may wish to determine a value for pressure at other locations. This can be accomplished by the method of linear interpolation.
In linear interpolation, the function is assumed to be piecewise linear between adjacent points in the domain, each identified by a domain coordinate value at which the function values are known. Thus, the relation of the interpolated value at a target point in the domain, that is, the domain coordinate value of the point in the domain at which the function value is to be interpolated, to the function values at the known points at adjacent domain coordinate value is linearly proportional to (1) the desired domain coordinate's relative distance from the known points, and (2) the difference between the values of the function at the two adjacent known points. Stated mathematically, in a one dimensional domain, this is ##EQU1## where f is the interpolated function, x.sub.1 and x.sub.2 are the domain coordinate values of the points at which the function values are known, and x.sub.d is the domain coordinate value at which the function value is being interpolated.
In the prior art, interpolation calculations have been performed by electronic computing systems. In these systems, the function values for the known points are stored in a single electronic memory. For each interpolation, this memory must be accessed twice, once to obtain a function value for each of the two known points with domain coordinates adjacent to the domain coordinate at which interpolation is to take place.